The sum of two angles is $94^\circ$. Angle 2 is $56^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 94}$ ${y = 2x-56}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-56}$ for $y$ in the first equation. ${x + }{(2x-56)}{= 94}$ Simplify and solve for $x$ $ x+2x - 56 = 94 $ $ 3x-56 = 94 $ $ 3x = 150 $ $ x = \dfrac{150}{3} $ ${x = 50}$ Now that you know ${x = 50}$ , plug it back into $ {y = 2x-56}$ to find $y$ ${y = 2}{(50)}{ - 56}$ $y = 100 - 56$ ${y = 44}$ You can also plug ${x = 50}$ into $ {x+y = 94}$ and get the same answer for $y$ ${(50)}{ + y = 94}$ ${y = 44}$ The measure of angle 1 is $50^\circ$ and the measure of angle 2 is $44^\circ$.